# Papers

## Planar diagrams for local invariants of graphs in surfaces

With Kyle Miller. *Journal of Knot Theory and its Ramifications*, 2019.

In order to apply quantum topology methods to non-planar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. We also discuss an extension of the flow polynomial called the S-polynomial and relate it to the Yamada and Penrose polynomials.

# Notes

## What is Lie algebra cohomology and why should you care?

Expository notes on Lie algebra cohomology. The goal is to build up the theory in as concrete a manner as possible, motivated by basic structure theorems for Lie algebras.